= Solution
The <Shapley value> is the expected <marginal contribution> of a player when the players join in uniformly random order. Equivalently,
$$
\phi_i(v)=\sum_{S\subseteq N\setminus\{i\}}\frac{|S|!(n-|S|-1)!}{n!}\bigl(v(S\cup\{i\})-v(S)\bigr).
$$
For three players, the weights for predecessor sets of sizes $0,1,2$ are $1/3,1/6,1/3$. Using the computed values,
$$
\begin{aligned}
\phi_1&=\tfrac13(0)+\tfrac16[(6-2)+(9-5)]+\tfrac13(15-11)=\tfrac83,\\
\phi_2&=\tfrac13(2)+\tfrac16[(6-0)+(11-5)]+\tfrac13(15-9)=\tfrac{14}3,\\
\phi_3&=\tfrac13(5)+\tfrac16[(9-0)+(11-2)]+\tfrac13(15-6)=\tfrac{23}3.
\end{aligned}
$$
Thus
$$
\boxed{\phi(v)=x:\quad\text{(b) is true.}}
$$
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